A body of mass $m$ is raised through a distance equal to the radius of the earth from the earth's su

Question

A body of mass $m$ is raised through a distance equal to the radius of the earth from the earth's surface. The change of potential energy will be\

Professor PC Thomas Classes · Answer

Gravitational PE of two masses $=\frac{G m_{1} m_{2}}{r}$ where $r$ is the distance between the masses. Let R be the radius of the earth\ PE on the ground $=\frac{-\mathrm{GMm}}{\mathrm{R}}$\ PE at height $\mathrm{R}=\frac{-\mathrm{GMm}}{2 \mathrm{R}}$\ Change of $\mathrm{PE}=\frac{-\mathrm{GMn}}{2 \mathrm{R}}-\left(\frac{-\mathrm{GMm}}{\mathrm{R}}ight)$\ $ \begin{aligned} & =\frac{\mathrm{GMn}}{\mathrm{R}}\left[1-\frac{1}{2}ight] \ & =\frac{\mathrm{GMm}}{\mathrm{R}} \frac{1}{2} \ & =\frac{1}{2}\left(\frac{\mathrm{GM}}{\mathrm{R}^{2}}ight) \mathrm{Rm}= \end{aligned} $